On the limit distribution for stochastic differential equations driven by cylindrical non-symmetric α-stable Lévy processes.

This paper deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical α -stable process. Under suitable conditions, it is proved that the solution of this equation converges weakly to that of a stochastic differential equation driven by a Brownian motion in the Skorohod space as α → 2. Also, the rate of weak convergence, which depends on 2 − α , for the solution towards the solution of the limit equation is obtained. For illustration, the results are applied to a simple one-dimensional stochastic differential equation, which implies the rate of weak convergence is optimal. [ABSTRACT FROM AUTHOR]